Cambridge IGCSE™

* 6 9 4 4 8 2 2 9 4 0 *

MATHEMATICS (US) 0444/23

Paper 2 (Extended) October/November 2022

1 hour 30 minutes

You must answer on the question paper.

You will need: Geometrical instruments

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, center number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● Calculators must not be used in this paper.
● You may use tracing paper.
● You must show all necessary work clearly.
● All answers should be given in their simplest form.

INFORMATION
● The total mark for this paper is 70.
● The number of marks for each question or part question is shown in parentheses [ ].

This document has 12 pages.

DC (RW/CT) 311546/2
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Formula List

- b ! b 2 - 4ac
For the equation ax 2 + bx + c = 0 x=
2a

Lateral surface area, A, of cylinder of radius r, height h. A = 2rrh

Lateral surface area, A, of cone of radius r, sloping edge l. A = rrl

Surface area, A, of sphere of radius r. A = 4rr 2

1
Volume, V, of pyramid, base area A, height h. V = Ah
3

1
Volume, V, of cone of radius r, height h. V = rr 2 h
3

4
Volume, V, of sphere of radius r. V = rr 3
3

A a b c
= =
sin A sin B sin C

a 2 = b 2 + c 2 - 2bc cos A
c b

1
Area = bc sin A
2
B a C

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1 Marco starts work at 20 45 and finishes at 02 08 the next day.

Find the length of time, in hours and minutes, he works.

..................... h .................... min [1]

2
117 121 149 164 215

From this list, write down

(a) a square number

................................................. [1]

(b) a prime number.

................................................. [1]

3 Work out.
0.000 009

................................................. [1]

4 The mean mass of four men in a rowing team is 100 kg.

The modal mass is 101 kg.
The range of the masses is 8 kg.

Find the mass of each of the four men.

................... kg , ................... kg , ................... kg, ................... kg [3]

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5 2
5 Work out - .
7 3
Give your answer as a fraction in its simplest form.

................................................. [2]

6 A spinner can land on the colors green, black or red.

The table shows the probabilities of the spinner landing on green or black.

Color Green Black Red

Probability 0.4 0.25

(a) Complete the table. [2]

(b) Chang spins the spinner 120 times.

Find the expected number of times it lands on green.

................................................. [1]

7 Find the least common multiple (LCM) of 36 and 60.

................................................. [2]

8 A is the point (-3, 5) and B is the point (5, 2).

Find the coordinates of the midpoint of the line AB.

( ..................... , ..................... ) [2]

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9 Solve the system of linear equations.

3x - 2y = 21
5x + 2y = 51

x = ................................................

y = ................................................ [2]

10

A B

Using compass and straight edge only, construct the circumscribed circle of triangle ABC. [4]

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11
NOT TO
SCALE
(7x + 76)°
(x + 8)°

The diagram shows two sides of a regular polygon.

The interior angle of the polygon is (7x + 76)° and the exterior angle is (x + 8)° .

Find the number of sides of this polygon.

................................................. [4]

12 Keita invests $4000 at a rate of 5% per year compound interest.

Work out the interest earned on the investment at the end of 2 years.

$ ................................................ [3]

13 Simplify 75 + 363 .

................................................. [2]

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14 A map has a scale of 1 : 200 000.

Find the area, in square kilometers, of a lake that has an area of 13 cm 2 on the map.

......................................... km 2 [2]

15

10

6
Speed
(m/s) 5

0
0 2 4 6 8 10 12 14 16 18 20
Time (seconds)

The graph shows the speed of a car as it slows down from a speed of 10 m/s until it stops at 20 seconds.

(a) Find the speed of the car at 14 seconds.

......................................... m/s [1]

(b) Find the average rate of change of the speed between 8 seconds and 10 seconds.

......................................... m/s 2 [2]

(c) By drawing a suitable tangent to the curve, find the rate of change of the speed at 8 seconds.

......................................... m/s 2 [2]

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16 A kite is drawn on a coordinate grid.

The diagonals of the kite intersect at the point (4, 7).

One diagonal has equation y = 2x - 1.

Find the equation of the other diagonal of the kite.

Give your answer in the form y = mx + b .

y = ................................................ [3]

17 y varies as the square of (x - 7) .

When x = 12, y = 2.

Find y when x = 17.

y = ................................................ [3]

18 Two bottles are mathematically similar.

The small bottle has a capacity of 270 ml and a height of 9 cm.
The large bottle has a capacity of 640 ml.

Work out the height of the large bottle.

............................................ cm [3]

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19 f (x) = 5x - 3, x 2 1
10
g (x) = , x!2
x-2
(a) Find g(f(x)).
Give your answer in its simplest form.

................................................. [2]

(b) Find g -1 (x) .

g -1 (x) = ................................................ [3]

(c) Find f (f -1 (x - 1)) .

................................................. [1]

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20 (a)

72° 48°

NOT TO
SCALE

x°

The diagram shows two straight lines crossing two parallel lines.

Work out the value of x.

x = ................................................. [2]

(b)

B
33° NOT TO
u° v° SCALE

w°
48°
A

The diagram shows a cyclic quadrilateral and its diagonals.

AB is a diameter.

Work out the values of u, v and w.

u = .................................................

v = .................................................

w = ................................................. [3]

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21 (a)
B
NOT TO
85° SCALE

65°
A C

C is due east of A.

Find the bearing of

(i) A from B

................................................. [1]

(ii) B from C.

................................................. [2]

(b)

8 cm 5 cm NOT TO
SCALE

30° x

Find the value of sin x.

................................................. [2]

Question 22 is printed on the next page.

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22 (a) Expand and simplify.

(3x + 1) (x - 2) - (x + 1) (2x - 3)

................................................. [3]

(b) Write as a single fraction in its simplest form.

4 2x 2 + 14x
' 2
2x - 3 2x + 11x - 21

................................................. [4]
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